The straightforward synthesis of nanoscale and (simultaneously) far-from-equilibrium solids is a great challenge despite promising developments of synthesis techniques (Bensch and Breu, 2017). Nanostructured compounds with a nonequilibrium short-range structure can hardly be accessed by conventional (thermal) solid-state preparation routes requiring high synthesis temperatures. Also wet (solution) chemistry-based preparation ways lead to the thermodynamically stable rather than metastable products. Fortunately, such hurdles can be overcome by chemical reactions initiated or accelerated by the direct absorption of mechanical energy (Baláž et al., 2013; Šepelák et al., 2013; Wilkening et al., 2017; Boldyrev, 2018). In addition, the mechanically induced chemical reactions often outperform their conventional and solution-based counterparts in terms of sustainability (Bolm and Hernández, 2018; Michalchuk et al., 2021). As a consequence, the mechanically induced chemistry (mechanochemistry) becomes a “game-changer” (Gomollón-Bel, 2019), especially in chemical synthesis (Avvakumov et al., 2001; Friščić et al., 2020; Lapshin et al., 2021). Mechanochemistry is currently undergoing rapid expansion in a number of areas, and has been applied for the synthesis of various compounds, including energy storage materials (Gombotz and Wilkening, 2021; Schlem et al., 2021), pharmaceutics (Solares-Briones et al., 2021), metal-organic frameworks (Zhou et al., 2019; Głowniak et al., 2021), organic compounds (Andersen and Mack, 2018; Michalchuk et al., 2019), catalytic materials (Pickhardt et al., 2020; Porcheddu et al., 2020; Amrute et al., 2021), nanocomposites (Sherif El-Eskandarany et al., 2021), and nanocrystalline inorganic materials (Šepelák et al., 2012a; Lunghammer et al., 2019; De Oliveira et al., 2020). From the point of view of the type of mechanical impact, the strategies to mechanically promote a chemical reaction in matter include the use of mechanical milling, extrusion techniques, pulsed ultrasonication, and single-molecule force spectroscopy approaches, among others (Lapshin et al., 2021; O’Neill and Boulatov, 2021).

The mechanochemical synthesis (sometimes shortly called mechanosynthesis), studied in the present work is a reduction-oxidation (redox) reaction via high-energy ball milling of a stoichiometric mixture of SrO, α-Fe and MoO₃ precursors at ambient temperature in air, leading to the formation of strontium ferromolybdate Sr₂FeMoO₆. Using the recently proposed pictographic nomenclature for mechanochemical syntheses (Michalchuk et al., 2021), the present redox reaction emphasizing the changes in valence state of the Fe and Mo cations can roughly be represented as 2 SrO + α-Fe⁰ + Mo⁶⁺O₃ + ½ O₂ →→ Sr₂Fe³⁺Mo⁵⁺O₆, where the symbols and specify the reaction conditions; namely, they denote the use of “planetary ball mill” and “ambient atmosphere,” respectively. Although in the last few years a surge of investigations in the field of mechanochemistry has resulted in the mechanosynthesis of a variety of complex oxides by forcing a system to acquire metastable and non-equilibrium configurations (Zhang and Saito, 2012; Šepelák et al., 2013; Wilkening et al., 2017; Porodko et al., 2021; Szczȩśniak et al., 2021; Tsuzuki, 2021; Šepelák et al., 2021), there is no report in the literature on the nonconventional mechanochemical route to synthesize Sr₂FeMoO₆. Commonly, this material is prepared via a conventional multi-step ceramic route (Valenzuela et al., 2014; Kalanda et al., 2019; Alvarado-Flores et al., 2021) or various wet chemistry-based routes (Li et al., 2019; Farzin et al., 2020; Valdés et al., 2021); some of them involve a prolonged heat treatment at considerably high temperatures under reducing atmosphere (Iranmanesh et al., 2016). The present work demonstrates that Sr₂FeMoO₆ can be mechanosynthesized at ambient temperature in air directly from its precursors in the form of nanostructured powders, without the need for solvents and/or calcination under controlled oxygen fugacity, thus making the process very facile and efficient.

From the point of view of mechanochemistry, an important question providing a part of motivation for the present work is, whether it is possible to transform, by means of a mechanochemical processing, zero-valent metallic iron (one of the reaction educts) into its three-valent (ferric) state present in the reaction product. To the best of our knowledge, a mechanochemical reaction leading to such a large extent of oxidation of iron species (Fe⁰ → Fe³⁺) has not yet been reported. Note that the Fe⁰ → Fe²⁺ transformation path has been observed to occur, for example, during the single-step mechanosynthesis of nanostructured Fe²⁺-containing α-Fe₂SiO₄ and Fe₂GeO₄, starting from the mixture of metallic Fe⁰ and corresponding precursors (Šepelák et al., 2012a; Šepelák et al., 2012b), and the mechanochemical reduction of metal sulphides to prepare nanocrystalline metals (Godočíková et al., 2004). On the other hand, the mechanochemical reduction processes leading to the Fe³⁺ → Fe²⁺ → Fe⁰ transformations have been reported for spinel ferrites MFe₂O₄ (M = Mg, Ni) (Menzel et al., 2001; Šepelák et al., 2002). The present work gives evidence of the fact that the unique mechanically triggered chemical reaction leading to the extensive oxidation of the Fe⁰ precursor is feasible. The evolution of the Sr₂FeMoO₆ phase during the mechanosynthesis as well as the far-from-equilibrium structural state of the reaction product are systematically monitored with X-ray diffraction (XRD) and a variety of comprehensive spectroscopic techniques including Raman spectroscopy, ⁵⁷Fe Mössbauer spectroscopy, and X-ray photoelectron spectroscopy (XPS).

A considerable interest in Sr₂FeMoO₆, from both fundamental and practical points of view, is prompted by the discovery of its room-temperature low-field magnetoresistance and half-metallicity (Kobayashi et al., 1998). Such properties predestinate this material for a variety of possible technological applications in the field of spintronics and solid oxide fuel cells (Kalanda et al., 2018; Huan et al., 2017; Skutina et al., 2021; Xi et al., 2021). Sr₂FeMoO₆ is an important member of the family of double perovskites with the general formula A ₂ BB′O₆ (A is a divalent alkaline earth cation; B and B′ are transition metal cations). It adopts the tetragonal crystal structure with space group I4/m (Nakamura and Oikawa, 2003), in which the twelve-fold coordinated Sr²⁺ cations reside in the cuboctahedral cavities created by the corner-sharing octahedra, while the octahedral sites are occupied by Fe and Mo ions. Despite its deceptively simple structure, Sr₂FeMoO₆ exhibits disordering phenomena involving the alternating positions of Fe and Mo atoms. In the fully ordered Sr₂FeMoO₆ double perovskite, Fe and Mo atoms alternate regularly along the c-axis of the tetragonal crystal lattice. Intervening O²⁻ ion bridges every Fe and Mo atom pair, thus forming the sequence of regularly alternating FeO₆ and MoO₆ octahedra along the c-axis (Figure 1). The cation disorder in Sr₂FeMoO₆, in which some Fe and Mo cations interchange their crystallographic positions, is referred to as anti-site disorder or mis-site disorder. The anti-site disordered regions (sometimes called “clusters” or “patches” (Menéndez et al., 2004)) can be easily visualized as islands consisting of oxygen octahedra whose centers are all occupied by Fe atoms or all by Mo atoms. The crystal chemical formula emphasizing the cation site occupancy in Sr₂FeMoO₆ may be written as Sr₂[Fe_Fe]_1-ASD[Fe_Mo]_ASD[Mo_Mo]_1-ASD[Mo_Fe]_ASDO₆, where [Fe_Fe], [Mo_Mo] and [Fe_Mo], [Mo_Fe] denote the cations on the “right” octahedral sites (Fe cation on Fe-site and Mo cation on Mo-site) and anti-sites (Fe cation on Mo-site and Mo cation on Fe-site), respectively. The symbol ASD represents the so-called degree of anti-site disorder defined as the fraction of Fe-sites occupied by Mo ions and vice versa. Theoretically, ASD takes a value from 0 to 0.5, i.e., 0 ≤ ASD ≤ 0.5. The value of ASD in Sr₂FeMoO₆ crucially depends on the conditions of its synthesis. For example, the lowest value (ASD = 0.025) has been found to be at an optimum synthesis temperature of about 1423 K for ceramics long-term annealed (up to 150 h) under oxygen-deficient conditions (Shimada et al., 2003; Huang et al., 2004). On the other hand, the considerably high values of ASD ranging from 0.345 to 0.45 have been reported for Sr₂FeMoO₆ prepared by melt-quenching method (Sarma et al., 2000a; Kobayashi et al., 2007). Here, we were able to mechanosynthesize the nanostructured and fully anti-site disordered Sr₂FeMoO₆ with a record-high value of ASD = 0.5. It should be emphasized that this value, derived independently from the present experimental XRD, Mössbauer, and magnetization data, is, to the best of our knowledge, the highest value so far reported for the Sr₂FeMoO₆ phase.

Anti-site defects are recognized to drastically influence the magnetism of Sr₂FeMoO₆ (Reyes et al., 2016; Kalanda et al., 2020). The present study demonstrates that an extraordinarily high ASD in the as-prepared double perovskite leads to the deterioration of its magnetic properties. The mechanosynthesized Sr₂FeMoO₆ exhibits superparamagnetism at room temperature arising from its nanoscale nature evidenced by high-resolution transmission electron microscopy (HRTEM).

For the mechanosynthesis of Sr₂FeMoO₆, the reactants SrO (Alfa Aesar), α-Fe (Alfa Aesar) and MoO₃ (Sigma-Aldrich) with the initial average particle sizes of 0.5, 0.7 and 0.3 μm, respectively, were mixed in a molar ratio of 2:1:1. The 2 SrO + α-Fe + MoO₃ mixtures were milled for various times t _M (up to 240 min) in a planetary ball mill Fritsch Pulverisette 7 Premium Line (Fritsch, Germany) at room temperature. The milling chamber (80 cm³ in volume) and 15 balls (10 mm in diameter), both made of tungsten carbide, were used. Milling experiments were performed in air at 500 rpm.

The XRD patterns were measured using a D8 Advance diffractometer (Bruker, Germany), operating in Bragg-Brentano configuration and using Cu Kα radiation. The XRD scans were collected from 10° to 70° (2 Theta), using a step of 0.03° and a data collection time of 12 s. The Powder Diffraction File (PDF) database (ICDD, Newtown Square, PA, United States) was utilized for phase identification. The tetragonal double perovskite structure of Sr₂FeMoO₆ was visualized using the Diamond program (Putz and Brandenburg, 2019).

Raman spectra were recorded using a micro-Raman multichannel spectrometer LabRam300 Infinity (Horiba Jobin Yvon, Japan) with the excitation wavelength of 532 nm (Nd:YAG laser). The Raman shift was calibrated using the Raman peak of silica wafer positioned at 520.7 cm⁻¹. The acquisition time and the number of scans were set to 10 and 7 s, respectively.

⁵⁷Fe Mössbauer spectra were taken in transmission geometry at room temperature (293 K) and 13 K. ⁵⁷Co in Rh matrix was used as the γ-ray source. Mössbauer data were fitted using the WinNormos software package (Wissel, Germany). The derived isomer shifts (IS) are given relative to IS of α-Fe at room temperature. The degree of anti-site disorder was calculated according to formula ASD = I[Fe_Mo]/2(I[Fe_Fe] + I[Fe_Mo]), where I[Fe_Mo] and I[Fe_Fe] are the relative intensities of Mössbauer subspectra corresponding to Fe ions on the Mo-sites and Fe-sites, respectively.

XPS measurements were performed using an XPS instrument SPECS (Specs, Germany) equipped with PHOIBOS 100 SCD and non-monochromatic X-ray source. The spectra were acquired at a basic pressure of 2 × 10⁻⁸ mbar with Mg Kα excitation at 10 kV. The spectrometer was calibrated against silver (Ag 3d). The data were analyzed using the SpecsLab2 CasaXPS software (Casa Software, United Kingdom).

HRTEM observations were performed employing a JEOL 2100F UHR microscope operated at 200 kV. High-resolution images were taken in a bright-field imaging mode. Prior to HRTEM investigations, powders were dispersed in ethanol and ultrasonicated for 10 min. Subsequently, a droplet of the water-diluted colloidal suspension was deposited on the copper-supported carbon grid. Finally, samples were stored in a vacuum chamber to evaporate residual ethanol.

Magnetic measurements were performed using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design MPMS-5S). The powdered samples were filled in a small gelatin capsule, whose diamagnetic moment was subtracted from the measured magnetization values. Magnetic hysteresis loops were recorded at 10 and 300 K in external magnetic fields from 0 to ±5 T. The temperature-dependent magnetic susceptibility was measured from 5 to 300 K in a magnetic field of 0.01 T.

The evolution of the 2 SrO + α-Fe + MoO₃ mixture milled in air was followed by XRD. Figure 2A shows XRD patterns of the mixture milled for various times. The XRD pattern of the starting powder (not shown) is characterized by sharp diffraction peaks corresponding to the solid reactants SrO (ICDD PDF 75-0263), α-Fe (06-0696) and MoO₃ (05-0508). During the early stages of milling (for t _M ≤ 15 min), XRD reveals a decrease in the intensity and an associated broadening of the Bragg peaks of the SrO and α-Fe educts, the complete disappearance of diffraction peaks assigned to the binary MoO₃ precursor, and the simultaneous formation of the intermediate ternary phase SrMoO₄ (08-0482); see Figure 2A (top). Note that a tiny fraction of Sr₃MoO₆ (27-1441) has also been detected in the sample milled up to 30 min. In analogy with our previous work on the mechanosynthesis of oxymolybdates (Tóthová et al., 2019) it can be assumed that a rapid formation of the ternary molybdates is accelerated by the emergence of the structurally disordered (or even amorphous) and, consequently, very reactive MoO₃ phase induced by mechanical action already in the early stages of milling process. For milling times t _M ≥ 30 min, qualitative changes are observed in the XRD patterns of the milled samples; clear evidence is observed of new diffraction features that correspond to the complete disappearance of the intermediates and the simultaneous formation of the Sr₂FeMoO₆ quaternary phase. In the XRD pattern of the mixture milled for 240 min (a product of the mechanochemical reaction), all diffraction peaks detected above the background are due to the tetragonal Sr₂FeMoO₆ phase (70-8133); see Figure 2A (bottom). Rietveld analysis of XRD data revealed the lattice parameters (a = 5.5856(5) Å, c = 7.8970(140) Å) and the random distribution of Fe and Mo cations (ASD = 0.5) in the mechanosynthesized Sr₂FeMoO₆. The latter will be discussed in detail concurrently with the analysis of the low-temperature ⁵⁷Fe Mössbauer spectroscopic data and SQUID magnetization data (see below).

To provide insight into the formation of intermediates in greater detail, the mechanochemical reaction 2 SrO + α-Fe + MoO₃ + ½ O₂ →→ Sr₂FeMoO₆ was also followed by Raman spectroscopy. Figure 2B compares Raman spectra of the 2 SrO + α-Fe + MoO₃ mixtures milled for various t _M. The spectrum of the starting mixture (t _M = 0 min) shows all Raman peaks typical for MoO₃ reactant. Note that the first-order Raman bands are neither expected for bcc structure of α-Fe nor for SrO being two remaining solid reactants (Mon, 1972). The strongest Raman peaks at 816 cm⁻¹ (with symmetries A _g, B _1g) and 994 cm⁻¹ (A _g, B _1g) evolve from the asymmetric and symmetric stretching of the terminal oxygen atoms in MoO₃, whereas the band at 665 cm⁻¹ (B _2g, B _3g) appears from the asymmetric stretching of the Mo–O–Mo bridge along the c-axis (Mestl et al., 1994). The lower wavenumber bands at 281 and 289 cm⁻¹ (B _2g, B _3g) are ascribed to the wagging modes of the terminal oxygen atoms, in addition to the 156 cm⁻¹ band (A _g, B _1g) that originates from the translation of rigid chains. An interesting observation is that already after 15 min of high-energy milling, all the Raman peaks assigned to the MoO₃ precursor disappear, and new bands at 880, 840, 790, and 320 cm⁻¹ evolve (Figure 2B). These bands are attributed to the formed SrMoO₄ intermediate phase (Sujatha et al., 2019). This finding supports and complements the above given XRD results, which reveal the complete and rapid reaction of MoO₃ and SrO precursors yielding the intermediate ternary molybdate SrMoO₄ already in the early stages of milling process. Further milling (t _M > 15 min) provokes significant changes in the Raman spectra; the most substantial feature is the appearance of a broad and intense complex band peaking at about 810 cm⁻¹ (ranging from about 850 to 770 cm⁻¹) that, in addition to the 440 cm⁻¹ weaker band, is characteristic for Sr₂FeMoO₆ (Son et al., 2001; Navarro et al., 2003). The broad shape of these Raman peaks reflects the structurally disordered nature of the final reaction product. Taking into account the results of the present XRD and Raman spectroscopic investigations, the overall reaction path leading to Sr₂FeMoO₆ and involving the formation of the SrMoO₄ intermediate can be expressed by the following sequence of two mechanochemical reactions: 2 SrO + α-Fe⁰ + Mo⁶⁺O₃ + ½ O₂ →→ SrO + α-Fe⁰ + SrMo⁶⁺O₄ + ½ O₂ →→ Sr₂Fe³⁺Mo⁵⁺O₆. The first reaction represents the mechanochemical synthesis of SrMo⁶⁺O₄, which is not accompanied by the valence change of the constituent cations, whereas the subsequent mechanochemical redox reaction includes the reduction of Mo⁶⁺ cations and the oxidation of Fe⁰ atoms. Note that a small amount of the SrMoO₄ intermediate remains unreacted in the sample milled up to 240 min (see a tiny Raman peak at 880 cm⁻¹ at the bottom of Figure 2B).

To determine the mechanically induced phase evolution of the 2 SrO + α-Fe + MoO₃ mixture from the point of view of the α-Fe precursor as an oxygen getter and to provide complementary insight into the short-range (local) structure of the formed Sr₂FeMoO₆ phase, the mechanochemical reaction was also followed by ⁵⁷Fe Mössbauer spectroscopy. This nuclear spectroscopic method has been proven to be well suited for the investigation of the charge state, the local coordination, and the magnetic state of iron ions in mechanosynthesized materials (Šepelák and Becker, 2000; Šepelák et al., 2006; Šepelák et al., 2007; Da Silva et al., 2011; Harris and Šepelák, 2018; Tóthová et al., 2018; Skurikhina et al., 2020). The room-temperature ⁵⁷Fe Mössbauer spectra illustrating the mechanically induced evolution of the 2 SrO + α-Fe + MoO₃ mixture are presented in Figure 3. As can be seen, the spectrum of the starting mixture shows a sextet with isomer shift IS = 0.02(1) mm/s and magnetic hyperfine field B _hf = 33.1(1) T corresponding to bcc metallic Fe in ferromagnetic state. With increasing t _M, the sextet becomes asymmetric toward the inside of each line, slowly collapses, and is gradually replaced by a central asymmetric doublet. In the spectrum of the sample milled for 240 min (see Figure 3, bottom), the sextet corresponding to α-Fe is not visible anymore and the central doublet becomes the only spectral component. Considering the relatively high ferrimagnetic-to-paramagnetic transition temperature of bulk (microcrystalline) Sr₂FeMoO₆ (T _c = 415 K (Kobayashi et al., 1998)), the presence of the doublet in the room-temperature ⁵⁷Fe Mössbauer spectrum of the sample milled for 240 min seems to be an unexpected finding. It can be understood to arise mostly from Fe cations in mechanosynthesized Sr₂FeMoO₆ nanoparticles exhibiting superparamagnetism (see below). Note that the latter arises if particle sizes are so small that thermally induced energy fluctuations (∼k _B T, where k _B is the Boltzmann constant and T is temperature) overcome the magnetic anisotropy energy (∼KV, where K is the anisotropy energy constant and V is the particle volume) and change the direction of the magnetization of a particle from one easy axis to another (Long, 1987). Similar magnetic relaxation phenomena and the complete absence of the magnetic hyperfine splitting at room temperature have been observed in other Fe-containing ultrafine-particle magnetics (e.g., ferrites) prepared via mechanosynthesis (Šepelák et al., 2006; Šepelák et al., 2007; Da Silva et al., 2011).

Since the relaxation time characterizing the superparamagnetic phenomenon is also a function of temperature (τ ∼ exp(KV/k _B T)) (Néel, 1949), the influence of superparamagnetic relaxation can be counteracted by reducing the sample temperature. Figure 4A presents the low-temperature (13 K) ⁵⁷Fe Mössbauer spectrum of the 2 SrO + α-Fe + MoO₃ mixture milled for 240 min. It is clearly visible that thermal fluctuations are suppressed at 13 K, and the Mössbauer spectrum of the sample consists of the superposition of three magnetic hyperfine splitting components (sextets). The hyperfine parameters resulting from the least-squares fitting of the spectrum are presented in Table 1. The first minor sextet (orange subspectrum with the relative intensity I[Fe_Fe] ∼ 5.9%) is assigned to the Fe cations in the ordered regions (clusters) of the mechanosynthesized Sr₂FeMoO₆ double perovskite with the regularly alternating corner-sharing FeO₆ and MoO₆ octahedra along the c-axis of its tetragonal crystal lattice. The value IS = 0.92(6) mm/s for this sextet corresponds to the state with a mixed valence of iron cations Fe²⁺/Fe³⁺ (between Fe²⁺ and Fe³⁺; sometimes formally denoted as Fe^2.5+) (Greneche et al., 2001; Menéndez et al., 2004). This degenerate nature of the fundamental state of iron cations in Sr₂FeMoO₆ is the result of the existing equilibrium Fe³⁺ + Mo⁵⁺ ↔ Fe²⁺ + Mo⁶⁺, in which the itinerant down-spin electron is shared by both types of atoms (Sarma et al., 2000b; Lindén et al., 2000).

The major component in the spectrum shown in Figure 4A (red subspectrum with the relative intensity I[Fe_Mo] ∼ 84.1%) is ascribed to the high-spin Fe³⁺ cations in octahedral coordination of oxygen anions in the anti-site disordered regions of the mechanosynthesized Sr₂FeMoO₆, where Mo-sites are occupied by Fe³⁺ cations and vice versa. From the relative intensities I[Fe_Mo] and I[Fe_Fe], the degree of anti-site disorder in the mechanosynthesized Sr₂FeMoO₆ is estimated to be ASD ∼ 0.467. Thus, the mechanosynthesized Sr₂FeMoO₆ can be considered as a nonequilibrium, highly disordered double perovskite possessing the almost random distribution of the Fe and Mo cations over the sites of octahedral coordination provided by the double perovskite structure. It should be noted that the iron nuclei located on the anti-sites ([Fe_Mo]) experience the most probable local magnetic hyperfine field B _hf = 49.0(3) T with a relatively broad field distribution of about 10 T (from about 45 to 55 T). This fact is a strong indication of both, the presence of a wide variation in the local chemical environment around Fe³⁺ cations from site to site and the presence of a strongly distorted geometry of FeO₆ octahedra in the anti-site disordered clusters of the mechanosynthesized material. This is in contrast to the iron cations located on the “right” octahedral sites ([Fe_Fe]), where the magnetic hyperfine field with the lower magnitude (B _hf = 46.4(1) T) and relatively narrow distribution of about 5 T is observed.

The Mössbauer active ⁵⁷Fe nuclei provide a very sensitive probe for the estimation of the yield of a mechanochemical formation reaction of Fe-containing compounds (Šepelák et al., 2006; Da Silva et al., 2011). The presence of the third sextet, that is assigned to metallic α-Fe nanoparticles (blue subspectrum with the relative intensity I _α-Fe ∼ 10% in Figure 4A), indicates that the present mechanochemical reaction is not completed after 240 min; its degree of conversion is about 90%. Note that this sextet is not present in the corresponding room-temperature Mössbauer spectrum (see Figure 3, bottom), confirming the superparamagnetic state of α-Fe nanoparticles in the mixture of the milled reactants. Taking into account that the present heterogeneous mechanochemical reaction involving solid precursors and the gaseous phase (oxygen) proceeds inside the closed milling chamber, it can be assumed that the further progress of the mechanosynthesis of Sr₂FeMoO₆ was hampered by the shortage of oxygen inside the chamber, and the reaction stopped after the full consumption of oxygen. However, the subsequent thermal treatment of the sample at a fairly moderate temperature of 923 K for 30 min in air leads to the further reaction of remaining α-Fe nanoparticles in the reaction mixture, and results in the full (100%) conversion of the reactants into the double perovskite Sr₂FeMoO₆ phase. This is documented in Figure 4B, where the low-temperature ⁵⁷Fe Mössbauer spectrum of the 2 SrO + α-Fe + MoO₃ mixture milled for 240 min taken after its thermal treatment is shown. The hyperfine parameters of the as-prepared Sr₂FeMoO₆ are listed in Table 1. It should be emphasized that the ⁵⁷Fe Mössbauer spectrum of the completely synthesized Sr₂FeMoO₆ consists of only one spectral component corresponding to the fully anti-site disordered Sr₂FeMoO₆ double perovskite with ASD = 0.5. This extraordinarily high value is, to the best of our knowledge, the highest value so far reported for the anti-site disordered Sr₂FeMoO₆ phase.

An interesting observation is that the moderate thermal tretament leads to the transformation of the small amount (∼5.9 wt.%) of the ordered Sr₂FeMoO₆ clusters into the anti-site disordered state. This unusual structural order-disorder transformation upon heating can be caused by the progression of concurrent reaction of remaining Fe⁰ (∼10 wt.%) in the reaction mixture. It seems that tiny metallic iron in superparamagnetic state with a large reaction surface and a high oxidation affinity plays an important role in the present mechanosynthesis of Sr₂FeMoO₆. Its mechanically induced steady presence in the reaction mixture of educts initiates/promotes the redox Fe⁰ → Fe³⁺ and Mo⁶⁺ → Mo⁵⁺ reactions.

To verify the valence state of the Fe and Mo ions in the as-prepared fully anti-site disordered double perovskite, information on its short-range structure, provided by the ⁵⁷Fe Mössbauer spectroscopic technique, is complemented by an investigation of the electronic state of the constituent cations by means of X-ray photoelectron spectroscopy. Figure 5 displays both the room-temperature ⁵⁷Fe Mössbauer and XPS spectra of the material. The ⁵⁷Fe Mössbauer spectrum (Figure 5A) consists of the symmetric doublet that is well fitted by only one spectral component with isomer shift IS = 0.35(5) mm/s and quadrupole splitting QS = 0.92(1) mm/s. The latter values of hyperfine parameters are characteristic of Fe³⁺ cations in octahedral coordination of oxygen anions (Menil, 1985). The presence of the doublet also reveals that, even after its moderate thermal treatment, the as-prepared fully anti-site disordered Sr₂FeMoO₆ double perovskite exhibits superparamagnetism at room temperature (see doublets in Figure 2 (bottom) and Figure 5A). This demonstrates a fairly good stability of the superparamagnetic material at moderate temperatures, and simultaneously indicates that the thermal treatment applied does not bring about a substantial growth of Sr₂FeMoO₆ nanoparticles (see also the detailed HRTEM analysis below). It is also worth to mention that the value of quadrupole splitting (QS ∼ 0.9 mm/s) for the as-prepared double perovskite is significantly larger than that observed for other superparamagnetic fine Sr₂FeMoO₆ nanoparticles (Yarmolich et al., 2016; Suominen et al., 2007). This variation is associated with the presence of strongly deformed FeO₆ octahedra in the mechanosynthesized perovskite, as it is derived from the low-temperature ⁵⁷Fe Mössbauer spectra presented in Figure 4. Note that the broadly distorted geometry of the constituent structural units (building blocks) is typical for nanosized particles prepared by mechanochemical routes, and it has been evidenced by nuclear spectroscopic methods in numerous far-from-equilibrium complex oxides (Šepelák et al., 2009; Šepelák et al., 2013; Da Silva et al., 2021). This is also in line with previous work on Sr₂FeMoO₆, where an important crystallographic distortion around Fe³⁺ cations is postulated due to highly unspherical electric fields generated by anti-side disorder (Greneche et al., 2001) or, alternatively, due to the existence of Mo vacancies (Chmaissem et al., 2000).

The Mo 3d core level XPS spectrum of the as-prepared Sr₂FeMoO₆ is displayed in Figure 5B. In the XPS spectrum of the initial 2 SrO + Fe + MoO₃ mixture (the spectrum not shown), the Mo 3d core electron level appears at the binding energies of 232.1 and 235.2 eV for 3d _5/2 and 3d _3/2 electronic states, respectively. These values are typical for the Mo⁶⁺ valence state in the MoO₃ educt (Maiti et al., 2019). With increasing milling time, i.e., with increasing amount of the Sr₂FeMoO₆ phase in the reaction mixture, the 3d _5/2 and 3d _3/2 electron sublevels shift to sligtly higher binding energies. For the mechanosynthesized Sr₂FeMoO₆, the structureless 3d _5/2 and 3d _3/2 peaks are observed at 232.6 and 235.7 eV, respectively, (see Figure 5B). Using the literature values for different Mo oxides (Sarma et al., 2000b; Jalili et al., 2009), the observed Mo 3d _5/2 and Mo 3d _3/2 features are ascribed to arise solely from the Mo⁵⁺ oxidation state. Note that the similar values of binding energies (232.2 and 235.3 eV) have been reported for the Mo⁵⁺ state in nanoscale thin films of Sr₂FeMoO₆ (Jalili et al., 2009). Thus, it is clear from the analyses given hitherto that the present mechanochemical redox reaction can be written as: 2 SrO + α-Fe⁰ + Mo⁶⁺O₃ + ½ O₂ →→ Sr₂Fe³⁺Mo⁵⁺O₆, where Mo⁶⁺ is reduced to Mo⁵⁺ and Fe⁰ is oxidized to Fe³⁺. To the best of our knowledge, the one-step mechanochemical synthesis accompanied by such a large extent of oxidation (Fe⁰ → Fe³⁺) has not yet been reported.

Taking into account that superparamagnetism, evidenced for the as-prepared materials by means of ⁵⁷Fe Mössbauer spectroscopy (see above), is the particle size (the particle volume) dependent phenomenon (Néel, 1949), HRTEM investigations of both the partly synthesized Sr₂FeMoO₆ (the 2 SrO + Fe + MoO₃ mixture milled for 240 min) and the completely synthesized Sr₂FeMoO₆ (the mixture milled for 240 min followed by its thermal treatment at 923 K for 30 min) were performed to uncover their morphology. The representative HRTEM micrographs of the as-prepared materials are shown in Figure 6. It is revealed that both materials consist of agglomerated fully crystalline nanoparticles. The partly synthesized Sr₂FeMoO₆ is found to exhibit a particle size distribution ranging from about 5 to 12 nm (an average particle size is estimated to be 9(2) nm) with the irregular particle shape and random orientation, whereas the completely synthesized Sr₂FeMoO₆ possesses a broader particle size distribution (7–28 nm) with the average particle size of about 21(4) nm and the roughly spherical particle shape. The relatively broad distribution of particle sizes can be a result of the heterogeneous nucleation-and-growth processes (Da Silva et al., 2011) of the product phase in the course of the mechanically induced formation reaction. In both cases, the high-resolution TEM images show lattice fringes corresponding to the crystallographic planes with Miller indices (012) (interplanar distance d ₍₀₁₂₎ = 0.36 nm) (Figure 6A) and (200) (d ₍₂₀₀₎ = 0.28 nm) (Figure 6B) of the Sr₂FeMoO₆ phase (ICDD PDF 70-8133). The lattice fringes cross the whole interior of particles demonstrating their single-crystalline character. Thus, it is evident now that the applied moderate thermal treatment of the partly synthesized Sr₂FeMoO₆ nanoparticles does not bring about their substantial growth; in the thermally treated sample, Sr₂FeMoO₆ nanoparticles are still sufficiently small to exhibit superparamagnetic state at room-temperature (see Figure 5A).

The temperature-dependent magnetization measurements were performed to confirm the superparamagnetic state of the as-prepared nanostructured Sr₂FeMoO₆. Figure 7A shows the zero-field-cooled (ZFC) and field-cooled (FC) magnetization curves of the nanomaterial measured in the temperature range from 5 to 300 K in an external magnetic field of 0.01 T. Above 5 K, the increase with temperature of the ZFC curve is an indicator of the appearance of superparamagnetism in Sr₂FeMoO₆ nanoparticles, which give rise to a single maximum at about T _s = 120 K (Hansen and Mørup, 1999). The latter is a critical point (the so-called blocking temperature) corresponding to the blocking (freezing of the magnetic moments) of the smallest nanoparticles in the double perovskite particulate system. The point at which the ZFC and FC curves start to coincide (T _B ∼ 240 K) is associated with the blocking temperature of the biggest Sr₂FeMoO₆ nanoparticles. The relatively large difference between T _s and T _B (∼120 K) indicates that the as-prepared double perovskite possesses a relatively broad distribution of particle sizes. The latter finding confirms the results of HRTEM investigations presented above. The presence of a single maximum in the ZFC curve points to a single-stage process of the nanoparticle blocking (Yu et al., 1999), which reflects a single-modal particle size distribution in the nanostructured material.

There is a strong correlation between the octahedral cation anti-site disorder in Sr₂FeMoO₆ and its magnetism (Kobayashi et al., 1998; Ogale et al., 1999; Reyes et al., 2016). The magnetic ground state of the fully ordered Sr₂FeMoO₆ is usually considered as a ferrimagnetic collinear state with parallel magnetic moments of Fe³⁺ cations (μ _Fe = 5 μ _B, μ _B is Bohr magneton; μ _B = 9.27408 × 10⁻²¹ emu), which are antiparallel to the moments of Mo⁵⁺ cations (μ _Mo = 1 μ _B) (Saloaro et al., 2016). Taking into account the formula Sr₂[Fe_Fe↑]_1-ASD[Fe_Mo↓]_ASD[Mo_Mo↓]_1-ASD[Mo_Fe↑]_ASDO₆, which emphasizes the cation site occupancy and the spin alignment in the anti-site disordered Sr₂FeMoO₆, the effective magnetic moment μ per formula unit (f.u.) of the material may be written as: μ   =   μ Fe ( 1 - A S D ) - μ Fe A S D - μ Mo   ( 1 - A S D ) + μ Mo A S D = μ Fe ( 1 - 2 A S D ) - μ Mo ( 1 - 2 A S D ) = ( μ Fe − μ Mo ) ( 1 - 2 A S D ) = 4 μ B ( 1 - 2 A S D ) = ( 4 - 8 A S D ) μ B

Thus, this simplified approach taking into account the spin-only contribution of cations and omitting the itinerant character of spin-down electrons shows that μ linearly decreases with increasing ASD. The effective magnetic moment μ = 4 μ _B/f.u. corresponds to the fully ordered double perovskite with ASD = 0 and μ = 0 for the fully disordered double perovskite with ASD = 0.5. The linear decrease of the saturation magnetization of Sr₂FeMoO₆ with increasing ASD has also been predicted on the basis of Monte Carlo simulations (Ogale et al., 1999) and ab initio calculations (Reyes et al., 2016). The degradation of magnetic properties of Sr₂FeMoO₆ with increasing cation disorder has also been confirmed experimentally in numerous papers, see, e.g., (Suchaneck et al., 2020).

The magnetization hysteresis loops of the as-prepared nanostructured Sr₂FeMoO₆ measured at 300 and 10 K are depicted in Figure 7B. As expected for magnetization measurements above T _B, the room-temperature hysteresis loop of the nanomaterial is dominated by the superparamagnetic relaxation effect, whereas a slight magnetic hysteresis is observed at 10 K. Thus, the room-temperature M(H _ext) curve was analyzed in terms of superparamagnetic behavior using the Brillouin function. The effective magnetic moment derived from the analysis attains the value μ = 0.055 μ _B/f.u. Using the above given relation μ = (4 – 8 ASD) μ _B and the experimentally determined magnetic moment μ = 0.055 μ _B, the value of ASD for the as-prepared Sr₂FeMoO₆ is estimated to be about 0.493. This value derived from SQUID measurements is in excellent agreement with that obtained from the present Mössbauer and XRD data (see above). This extraordinarily high degree of anti-site disorder in the as-prepared nanostructured Sr₂FeMoO₆ corresponds to the completely random distribution of cations with a maximum configurational entropy. It should be emphasized that the nearly random distribution of cations has also been reported for spinel oxides prepared by mechanochemical routes (Šepelák et al., 2013).

The high-energy milling of the 2 SrO + α-Fe + MoO₃ mixture at ambient temperature in air leads to the mechanochemical synthesis of the tetragonal double perovskite Sr₂FeMoO₆ with the lattice parameters a = 5.5856(5) Å and c = 7.8970(140) Å. The overall reaction path leading to Sr₂FeMoO₆ involves the formation of the intermediate SrMoO₄ ternary phase, and can be expressed by the following sequence of two mechanochemical reactions: 2 SrO + α-Fe⁰ + Mo⁶⁺O₃ + ½ O₂ →→ SrO + α-Fe⁰ + SrMo⁶⁺O₄ + ½ O₂ →→ Sr₂Fe³⁺Mo⁵⁺O₆. The first one represents the mechanochemical synthesis of the intermediate SrMo⁶⁺O₄ phase, which is not accompanied by the valence change of the constituent cations, whereas the subsequent mechanochemical redox reaction includes the reduction of Mo⁶⁺ cations and the oxidation of Fe⁰ atoms. This unique mechanochemical synthesis accompanied by such a large extent of oxidation (Fe⁰ → Fe³⁺) has not yet been reported. The degree of conversion of the present mechanochemical synthesis is estimated to be about 90%. The subsequent thermal treatment of the mechanically activated material at a fairly moderate temperature of 923 K for 30 min in air results in the full conversion of the reactants into the double perovskite Sr₂FeMoO₆ phase. Despite the latter processing, the completely synthesized Sr₂FeMoO₆ possesses the nanostructured nature characterized by a relatively broad particle size distribution (7–28 nm) with the average particle size of about 21(4) nm and the roughly spherical particle shape. The degree of anti-site disorder in the as-prepared Sr₂FeMoO₆ is found to be ASD = 0.5, demonstrating its far-from-equilibrium, highly disordered structural state possessing the completely random distribution of Fe³⁺ and Mo⁵⁺ cations over the sites of octahedral coordination provided by the double perovskite structure. It should be emphasized that this record-high value of ASD = 0.5, derived independently from the present experimental XRD, Mössbauer, and magnetization data, is, to the best of our knowledge, the highest value so far reported for the Sr₂FeMoO₆ phase. At the short-range scale, the iron nuclei located on the anti-sites ([Fe_Mo]) experience a relatively broad distribution of magnetic hyperfine fields of about 10 T (from about 45 to 55 T) reflecting both, the presence of a wide variation in the local chemical environment around Fe³⁺ cations from site to site and the presence of a strongly distorted geometry of the constituent FeO₆ octahedra. The nanostructured and fully anti-site disordered Sr₂FeMoO₆ exhibits the superparamagnetic behavior with the blocking temperature of about T _B = 240 K and the effective magnetic moment μ = 0.055 μ _B/f.u.